Simplify the following expression: $ t = \dfrac{-7p}{-5p + 7} + \dfrac{-9}{4} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-7p}{-5p + 7} \times \dfrac{4}{4} = \dfrac{-28p}{-20p + 28} $ Multiply the second expression by $\dfrac{-5p + 7}{-5p + 7}$ $ \dfrac{-9}{4} \times \dfrac{-5p + 7}{-5p + 7} = \dfrac{45p - 63}{-20p + 28} $ Therefore $ t = \dfrac{-28p}{-20p + 28} + \dfrac{45p - 63}{-20p + 28} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{-28p + 45p - 63}{-20p + 28} $ $t = \dfrac{17p - 63}{-20p + 28}$ Simplify the expression by dividing the numerator and denominator by -1: $t = \dfrac{-17p + 63}{20p - 28}$